On matroid modularity and the coefficients of the inverse Kazhdan-Lusztig polynomial of a matroid

Abstract

Following the work of Gao and Xie in [2], we state some properties of the inverse Kazhdan-Lusztig polynomial of a matroid. We also give partial answers to a conjecture that states that regular connected matroids are non-degenerate. We link the degeneracy of a matroid to the inverse Kazhdan-Lusztig polynomial and we show that the Conjecture holds for modular matroids, by proving that degenerate modular matroids are not regular.

9 pages v2 updated after mistake was found in a proof v3 section of new results expanded and divided into two new sections; added new results of non-degeneracy on even-rank matroids

References in corpus (2)

• Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures
• The inverse Kazhdan-Lusztig polynomial of a matroid